Math Problem Statement

find reference angle for 8pi/5

Solution

To find the reference angle for 8π5\frac{8\pi}{5}, follow these steps:

  1. Identify the quadrant: Since 8π5\frac{8\pi}{5} is greater than π\pi (which equals 5π5\frac{5\pi}{5}) but less than 2π2\pi (which equals 10π5\frac{10\pi}{5}), the angle lies in the third quadrant.

  2. Find the reference angle: The reference angle in the third quadrant is found by subtracting π\pi (or 5π5\frac{5\pi}{5}) from 8π5\frac{8\pi}{5}: Reference angle=8π5π=8π55π5=3π5\text{Reference angle} = \frac{8\pi}{5} - \pi = \frac{8\pi}{5} - \frac{5\pi}{5} = \frac{3\pi}{5}

So, the reference angle is 3π5\frac{3\pi}{5}.

Would you like further details or have any questions about this process?

Here are five related questions to explore further:

  1. What is the reference angle for 9π4\frac{9\pi}{4}?
  2. How do you calculate reference angles in the fourth quadrant?
  3. Can you determine the reference angle for 330330^\circ?
  4. What are the reference angles for negative angles?
  5. How do reference angles relate to trigonometric function values?

Tip: Reference angles are always positive and lie between 00 and π2\frac{\pi}{2} (or between 0° and 90° in degrees).

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Trigonometry
Reference Angles
Radian Measure

Formulas

Reference angle in quadrant III: θ - π
Reference angle in radians: θ' = θ - π (for third quadrant)

Theorems

Reference Angle Theorem

Suitable Grade Level

Grades 10-12